1but one Point only. For let it be de
68[Figure 68]
mitted into the Liquid, as hath been
ſaid; and let it firſt be ſo inclined, as
that its Baſe do not in the leaſt
touch the Surface of the Liquid. And
then it being cut thorow the Axis,
by a Plane erect unto the Surface of
the Liquid, let the Section of the
Portion be A N Z G; that of the
Liquids Surface E Z; the Axis of
the Portion and Diameter of the
Section B D; and let B D be cut in
the Points K and R, as before; and
draw N L parallel to E Z, and touching the Section A N Z G
in N, and N S perpendicular to
69[Figure 69]
B D. Now, ſeeing that the Por
tion is in Gravity unto the Liquid,
as the Square made of the Line
is to the Square B D; ψ ſhall
be equall to N T: Which is to
be demonſtrated as above: And,
therefore, N T is alſo equall to
V I: The Portions, therefore,
A V Q and E N Z are equall to
one another. And, ſince that in
the Equall and like Portions A V
Q L and A N Z G, there are drawn A Q and E Z, cutting off
equall Portions, that from the
70[Figure 70]
Extremity of the Baſe, this not
from the Extreme, that which is
drawn from the Extremity of the
Baſe, ſhall make the Acute Angle
with the Diameter of the Portion
leſſer: and in the Triangles N L S
and V ω C, the Angle at L is
greater than the Angle at ω:
Therefore, B S ſhall be leſſer
than B C; and S R leſſer than
C R: and, conſequently, N X
greater than V H; and X T leſſer than H I. Seeing, therefore,
that V Y is double to Y I; It is manifeſt, that N X is greater than
double to X T. Let N M be double to M T: It is manifeſt, from what
hath been ſaid, that the Portion ſhall not reſt, but will incline, untill
that its Bafe do touch the Surface of the Liquid: and it toucheth it in
one Point only, as appeareth in the Figure: And other things
68[Figure 68]mitted into the Liquid, as hath been
ſaid; and let it firſt be ſo inclined, as
that its Baſe do not in the leaſt
touch the Surface of the Liquid. And
then it being cut thorow the Axis,
by a Plane erect unto the Surface of
the Liquid, let the Section of the
Portion be A N Z G; that of the
Liquids Surface E Z; the Axis of
the Portion and Diameter of the
Section B D; and let B D be cut in
the Points K and R, as before; and
draw N L parallel to E Z, and touching the Section A N Z G
in N, and N S perpendicular to
69[Figure 69]B D. Now, ſeeing that the Por
tion is in Gravity unto the Liquid,
as the Square made of the Line
is to the Square B D; ψ ſhall
be equall to N T: Which is to
be demonſtrated as above: And,
therefore, N T is alſo equall to
V I: The Portions, therefore,
A V Q and E N Z are equall to
one another. And, ſince that in
the Equall and like Portions A V
Q L and A N Z G, there are drawn A Q and E Z, cutting off
equall Portions, that from the
70[Figure 70]Extremity of the Baſe, this not
from the Extreme, that which is
drawn from the Extremity of the
Baſe, ſhall make the Acute Angle
with the Diameter of the Portion
leſſer: and in the Triangles N L S
and V ω C, the Angle at L is
greater than the Angle at ω:
Therefore, B S ſhall be leſſer
than B C; and S R leſſer than
C R: and, conſequently, N X
greater than V H; and X T leſſer than H I. Seeing, therefore,
that V Y is double to Y I; It is manifeſt, that N X is greater than
double to X T. Let N M be double to M T: It is manifeſt, from what
hath been ſaid, that the Portion ſhall not reſt, but will incline, untill
that its Bafe do touch the Surface of the Liquid: and it toucheth it in
one Point only, as appeareth in the Figure: And other things